Correct Answer - Option 2 : 11.08 m/s
2
The correct answer is option 2) i.e. 11.08 m/s2
CONCEPT:
-
Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.
It is given mathematically as follows:
\(F = \frac{Gm_1m_2}{R^2}\)
Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.
- From the Law of Universal Gravitation, the gravitational force acting on an object of mass m placed on the surface of Earth is:
\(F = \frac{GMm}{R^2}\)
Where R is the radius of the earth.
From Newton's second law, F = ma = mg
\(⇒ mg =\frac{GMm}{R^2}\)
⇒ Acceleration due to gravity, \(g =\frac{GM}{R^2}\)
CALCULATION:
Let M be the mass of Earth, R be its radius and g be the acceleration due to gravity of Earth.
When the radius shrink by 5%, the new radius R' = 95%R = 0.95R
The mass remains the same i.e. M' = M
Initially, \(g =\frac{GM}{R^2} =10 \: m/s^2\)
After shrinking the radius, \(g' =\frac{GM'}{R'^2} \)
\(\Rightarrow g' =\frac{GM}{(0.95R)^2} =\frac{GM}{0.9025R^2}\)
\(\Rightarrow g' = \frac{g}{0.9025} = \frac{10}{0.9025} = 11.08 \:m/s^2\)
